Crescent Overlap Geometry Calculator
Ideal crescent subtracting overlap of two offset discs; containment, concentricity and disjoint cases explicit, no national construction standard inferred.
Description
An ideal crescent can be modeled as an outer disc with the overlapping part of a second disc removed.
An ideal crescent can be modeled as an outer disc with the overlapping part of a second disc removed.1
Containment and disjoint cases need explicit treatment before using the partial-overlap formula.
When to use Crescent Overlap Geometry Calculator
Use this tool when you need to reproduce the stated calculation from measured records or independently selected model inputs. Establish the flag dimensions, orientation, specification, palette, or visual annotations needed for this particular calculation.
How to use Crescent Overlap Geometry Calculator and understand its results
- Establish the flag dimensions, orientation, specification, palette, or visual annotations needed for this particular calculation.
- Enter outerRadius, cutoutRadius, centerSeparation, following the field table and rules below, then run the tool.
- Read result. Use the output meanings below to interpret units, signs, flags, and any nested result fields.
- Correct reported input issues and run again. For a successful result, check the stated evidence coverage and assumptions before using it in your review.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| outerRadius | Outer radius | number | Required |
| cutoutRadius | Cutout radius | number | Required |
| centerSeparation | Center separation | number | Required |
Use positive outer and cutout radii and nonnegative center separation in one unit. Normalize by the largest length for calculation. Disjoint discs have zero overlap; containment uses the smaller disc area; partial overlap uses two circular sectors minus the lens triangles. Return overlap and outer area minus overlap, floored at zero.
crescentArea=max(0,πr²−discOverlap(r,s,d)) Symbols follow the input and output meanings and the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Calculated observation or reference | object |
| result.circularOverlapArea | Circular Overlap Area | number |
| result.remainingCrescentArea | Remaining Crescent Area | number |
{
"input": {
"outerRadius": 10,
"cutoutRadius": 10,
"centerSeparation": 10
},
"output": {
"result": {
"circularOverlapArea": 122.83696986087571,
"remainingCrescentArea": 191.3222954981036
}
}
}Limitations and assumptions
The calculation uses supplied geometry, observations, or annotations. It does not establish an official construction specification, national identity, or universal design quality.
Missing required fields, unknown fields, wrong types, and violated calculation rules are input issues. Numeric values must be finite; nonfinite results are rejected. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related review, use Rising Sun Disc Offset Calculator: A rising-sun disc can lie partly above a horizontal horizon. Its center and radius determine an ideal circular segment area in a top-left coordinate frame with y increasing downward. For a complementary step, use Circle of Stars Ring Radius Calculator: A circle of star centers must leave room for each star’s radial extent and an edge margin. The available diameter therefore bounds the radius of the center ring.
References
-
Crescent Overlap Geometry Calculator — tool.io
Similar or alternative tools
- Rising Sun Disc Offset Calculator
A rising-sun disc can lie partly above a horizontal horizon. Its center and radius determine an ideal circular segment area in a top-left coordinate frame with y increasing downward.
- Circle of Stars Ring Radius Calculator
A circle of star centers must leave room for each star’s radial extent and an edge margin. The available diameter therefore bounds the radius of the center ring.